Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise
By Nathan E. Glatt-Holtz, Vlad Vicol. 2011
149 citations recorded by the source corpus.
We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a very general nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Lastly, we show that, in the three dimensional case, the addition of linear multiplicative noise provides a regularizing effect; the global existence of solutions occurs with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/f41b84cee1531d1fadf5ef1447752247276fc4ae
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In Applied Mathematics
- Xiangchan Zhu
- Rongchan Zhu
- Martina Hofmanov'a
- Eduard Feireisl
- Dominic Breit
- Xianpeng Hu
- Dehua Wang
- Didier Bresch
In Computational Theory and Mathematics
In Finance
Citations in the corpus
- On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations (2020, methodology): “ations treat only the two dimensional case (see e.g. [Be99, BF99, BP01, GHV14, BFM16]). The three-dimensional case has been treated in [MV00, Ki09, GHV14, CFH19]. In particular, Glatt-Holtz and Vicol [GHV14] obtained local well-posedness of strong solutions to stochastic Euler equations in two and t”
- On solvability and ill-posedness of the compressible Euler system subject to stochastic forces (2017, background): “ [19]. For completeness, let us mention that (1.4) may be seen as a “damping” term, the regularizing effect of which in the context of incompressible fluids has been recognized by Glatt–Holtz and Vicol [17], and for a general symmetric hyperbolic system by Kim [19]. To be more precise, in [19] it was ”